Hypothyroidism: This condition is common in menopausal women and can cause hypoglycemia, dry and brittle hair, dry skin, and fatigue. The recent change in hair and skin, along with frequent UTIs (which could be related to decreased estrogen levels), makes hypothyroidism a strong candidate.

Diabetes Mellitus: Although it might seem counterintuitive, diabetes can sometimes present with hypoglycemic episodes, especially if the patient is on insulin or oral hypoglycemic agents. The symptoms of fatigue and frequent UTIs could be related to diabetes.
Polycystic Ovary Syndrome (PCOS): Although PCOS is more commonly diagnosed in younger women, it can persist into menopause. It is associated with insulin resistance, which can lead to hypoglycemic episodes, and also with hormonal imbalances that could explain the hair and skin changes.
Adrenal Insufficiency: This condition can cause hypoglycemia, fatigue, and changes in skin and hair. However, it is less common than hypothyroidism and would typically present with additional symptoms such as weight loss and orthostatic hypotension.

Pituitary Tumor: A tumor in the pituitary gland can lead to multiple endocrine deficiencies, including adrenal insufficiency and hypothyroidism, causing hypoglycemia. It's crucial to consider this diagnosis due to its potential severity and the need for prompt treatment.
Cancer (e.g., Pancreatic Cancer): Certain cancers, particularly pancreatic cancer, can cause hypoglycemia. Given the potential lethality of cancer, it's essential to consider it in the differential diagnosis, even if it seems less likely.
Severe Liver Disease: Liver disease can lead to hypoglycemia due to impaired glucose production. While less common, it's a critical diagnosis not to miss due to its severity and the need for specific management.

Congenital Adrenal Hyperplasia (Late-Onset): This genetic disorder can lead to adrenal insufficiency and is associated with hypoglycemia. It's rare but should be considered in patients with unexplained hypoglycemia and other suggestive symptoms.
Insulinoma: A rare tumor of the pancreas that produces excess insulin, leading to hypoglycemia. It's an important diagnosis to consider due to its specific treatment requirements, despite its low incidence.